E-raamat: Dynamics of Fixed Marine Structures

Foreword Preface1 Introduction 1.1 Outline of the contents 1.2
Layout 1.3 Sections which help with the selection of analysis strategy
1.4 Use of the book as a technical reference 1.5 Use of the book as an
introductory text2 Dynamics with deterministic loading 2.1 Linear single
degree of freedom systems: SDOF 2.1.1 Units 2.2 Oscillation of
an SDOF with neither forcing nor damping 2.3 Steady state oscillation of
an SDOF with forcing and viscous damping 2.3.1 Steady state
solution using real algebra 2.3.2 Dynamic amplification factor
2.3.3 Significance of forcing and natural frequencies 2.3.4
Steady state solution using complex algebra 2.3.5 Complex number
representation of response 2.3.6 Steady state response of a
non-linear SDOF 2.4 Damped decay and build-up of oscillation
2.4.1 Viscous, damped decay of oscillation 2.4.2 Damping ratio and
logarithmic decrement 2.4.3 Response to an impulse 2.4.4
Viscous damped build-up of natural frequency oscillation 2.5 Damping
2.5.1 Hysteretic damping 2.5.2 Friction damping
2.5.3 Typical structural damping 2.6 Modeling multidegree of freedom
structures: MDOFs 2.6.1 Natural frequencies of a 2 degree of
freedom system 2.6.2 Modeling frame structures 2.6.3 Beam
element stiffness 2.6.4 Global axes 2.6.5 Axis
transformation 2.6.6 Assembly of global stiffness matrix
2.6.7 Damping 2.6.8 Mass 2.6.9 Supports 2.6.10
Forces applied at nodes 2.6.11 Forces applied to members
2.6.12 Constraints 2.6.13 Joints 2.6.14 Geometric
stiffness 2.6.15 Hydrostatic stiffness and effective tension
2.6.16 Modeling continuous structures using plate, shell and brick elements
2.6.17 Substructures 2.7 Static analysis of MDOF structures
2.7.1 Quasi-static analysis 2.8 Steady state solution using
complex matrix algebra 2.9 Natural frequencies of MDOFs 2.9.1
Eigenvalue form 2.9.2 Jacobi method 2.9.3 Householder
QR/QL method 2.9.4 Polynomial solution 2.9.5 Vector
iteration methods 2.9.6 More complicated methods 2.9.7
Selection of frequency/mode shape calculation method 2.9.8 Some
frequencies of commonly used structural elements 2.10 Normal mode (or
principal or generalized) coordinates 2.10.1 Forced vibration of
MDOF systems 2.10.2 Other uses of principal/generalized coordinates
2.11 Time history solution methods 2.11.1 Convolution integral
2.11.2 Time stepping methods 2.11.3 Central difference
(explicit) method 2.11.4 Runge-Kutta (explicit) method
2.11.5 Newmark ß (implicit) method 2.12 Economic solution of large
dynamic problems 2.12.1 Separate, simpler model 2.12.2
Guyan reduction or static condensation 2.12.3 Static improvement
Notation Bibliography References 3 Statistical and spectral
description of random loading and response 3.1 Short term, frequency and
sequence independent properties of y(t) 3.1.1 Measures of location
3.1.2 Measures of spread 3.1.3 Probability density
function (PDF) 3.1.4 Cumulative distribution function (CDF)
3.1.5 Moments of a PDF 3.1.6 Gaussian (normal distribution)
3.1.7 Non-Gaussian distributions 3.2 Sequence dependent properties
of a time history y(t) 3.2.1 Autocovariance 3.2.2
Autocorrelation function Ryy(x) 3.2.3 Autocorrelation coefficient
or normalised autocovariance 3.2.4 Time scale 3.3 Fourier
analysis and spectra of y(t) 3.3.1 Fourier series 3.3.2
Fourier transform representation of a random time history 3.3.3
Alternative forms of the Fourier transform 3.3.4 The discrete
Fourier transform 3.3.5 The Fourier transform pair 3.3.6
Integral form of the Fourier transform pair 3.3.7 Spectral density
3.3.8 Spectral analysis of a dynamic system subject to loading
defined by one variable 3.4 Relationship between autocovariance and the
energy spectrum 3.5 Short term frequency and sequence independent
statistics of simultaneous samples from several time histories: y^t), y2(t)
... 3.5.1 Covariance of yx(t) and y2(t) 3.5.2 Correlation
coefficient or normalised covariance 3.5.3 Statistical properties
of a + byt(t) + cy2(t) 3.5.4 Statistical properties of y^t) x y2(t)
3.5.5 Joint probability of n random variables 3.5.6
Gaussian multivariate distribution 3.6 Sequence dependent properties of
samples from several time histories 3.6.1 Cross-covariance
3.6.2 Cross-correlation coefficient or normalised cross-covariance
3.6.3 Cross-correlation function 3.6.4 Nomenclature 3.7 Cross
spectral density and coherence 3.7.1 Cross spectral density
3.7.2 Single-sided cross spectral density 3.7.3 Co- and
quad-spectral density 3.7.4 Coherence 3.7.5 Spectral
analysis of the response to a summation of random signals 3.8
Relationship between the cross-covariance and the cross-spectrum 3.9
Some further derivations based on spectral properties 3.9.1
Velocity and acceleration spectra 3.9.2 Spectral moments
3.9.3 Bandwidth 3.9.4 Crossing periods and peak distributions
3.9.5 Level crossing periods and the zero crossing period Tz
3.9.6 The crest frequency fc and period Tc 3.9.7 Distribution of
amplitudes in a narrow banded spectrum 3.9.8 Rayleigh distribution
3.9.9 Predicting the amplitude exceeded with a given probability or
in a given number of cycles 3.9.10 Distribution of the extreme
values of a Rayleigh distribution 3.10 Extreme value distributions for
environmental data 3.10.1 Types of extreme value distribution
3.10.2 Selection of extreme value distribution 3.10.3 Return
period Notation Commonly used symbols Summary
Bibliography References 4 Structural response to random loading 4.1
Wave, wind and earthquake - differences leading to different analysis methods
4.2 Structural response in waves, wind and earthquake 4.2.1
Structural response to a unidirectional sea 4.2.2 Structural
response to wind turbulence 4.2.3 Structural response to
earthquakes 4.2.4 Structural response to waves, wind and
earthquake: summary 4.3 Examples of non-linearities 4.3.1 The
effect of non-linear drag loading 4.3.2 The effect of intermittent
loading in the splash zone 4.3.3 The effect of non-linear drag for
a structure in the wind 4.3.4 The effect of non-linear guy wire
behavior on a structure in the wind 4.3.5 The effect of yielding on
a structure in an earthquake 4.4 Time history analysis methods
4.4.1 Time history analysis of a structure in a unidirectional sea
4.4.2 Time history analysis of a structure in a spread sea 4.4.3
Time history analysis of a structure in a turbulent wind 4.5 Conclusion
Notation References 5 Foundations 5.1 Introduction
5.1.1 Safety factors for foundations 5.2 Introduction to soil behavior
5.2.1 Permeability 5.2.2 Effective stress 5.2.3
Failure of soils 5.2.4 Mohr's circle 5.2.5 Application of
Mohr's circle in conjunction with the soil failure criterion 5.2.6
Drained and undrained loading and liquefaction of sands 5.2.7
Consolidation of clays 5.2.8 Soil structure, relative density and
clay remolding 5.2.9 Stiffness of soils 5.2.10 Soil
damping 5.2.11 Indicative soil properties 5.3 Site
investigation and testing 5.3.1 In-situ measurements
5.3.2 Laboratory tests for soil strength 5.3.3 Consolidated-drained
(CD) triaxial test 5.3.4 Consolidated-undrained (CU) triaxial test
5.3.5 Unconsolidated-undrained (UU) triaxial test 5.3.6
Unconfined compression test 5.3.7 Differences between soil
properties estimated from drained and undrained tests 5.4 Stability of
the seabed surface 5.4.1 Scour 5.4.2 Mudslides
5.4.3 Sand waves, dunes, banks, etc. 5.4.4 Subsidence 5.5
Gravity structures 5.5.1 Finite element (FE) methods
5.5.2 Half-space theory 5.5.3 Ultimate capacity of gravity
foundations 5.5.4 Piping 5.5.5 Effect of consolidation on
bearing capacity 5.5.6 Bearing capacity from published factors
5.5.7 Bearing capacity calculated by the method of slices
5.5.8 More advanced analysis of foundation capacity 5.5.9 Jack-up
platforms 5.6 Single piles 5.6.1 Development of lateral
force-deflection (p-y) curves 5.6.2 Calculation of Pu
5.6.3 p-y curve for clay 5.6.4 p-y behavior in clay under cyclic
conditions 5.5.5 Effect of consolidation on bearing capacity
5.6.6 Compression capacity of piled foundations 5.6.7 Tension
capacity 5.6.8 Scour and cavities 5.6.9 Shaft resistance
in sand 5.6.10 Shaft resistance in clay 5.6.11 Shaft
resistance - displacement (t-z) curves 5.6.12 End bearing capacity
of piles 5.6.13 Axial end bearing - displacement (q-z) curves
5.6.14 Torsional moment-rotation curves 5.6.15 Piles in
calcareous soils 5.7 Including foundation behavior in global structural
analysis 5.7.1 The use of substructuring for the quasi-static
analysis of structures on piled foundations 5.7.2 Linearized
foundation tangent stiffness for quasi-static analysis of structures on piled
foundations 5.7.3 Linearized foundation secant stiffness for
dynamic analysis of structures on piled foundations 5.8 Pile groups
5.8.1 Pile group axial capacity 5.8.2 Pile group lateral
capacity 5.8.3 Force-deflection analysis of piles in groups
Notation References 6 Waves and wave loading 6.1 Introduction
6.2 Waves and currents 6.2.1 Regular waves 6.2.2 Particle
motions 6.2.3 Mass transport 6.2.4 Group velocity CG
6.2.5 Ocean waves 6.2.6 Sea 6.2.7 Swell
6.2.8 Significant wave height and mean zero crossing period 6.2.9
Spectrum 6.2.10 Scatter diagrams 6.2.11 Persistence
diagrams 6.2.12 Sea-state cycles 6.2.13 Effect of the
seabed on wave characteristics 6.2.14 Shoaling 6.2.15
Diffraction 6.2.16 Refraction 6.2.17 Reflection
6.2.18 Absorption 6.2.19 Wave breaking 6.2.20 Currents
6.3 Measurement 6.3.1 Water surface elevation 6.3.2
Water particle velocities 6.4 Forecasting 6.4.1 General
6.4.2 Extrapolation to extreme values from measurements 6.4.3
Obtaining a long term description of the sea from measurements
6.4.4 Forecasting wave height and period from wind and fetch 6.4.5
Forecasting long term statistics of wave height and period 6.4.6
Forecasting currents 6.4.7 Computer modeling 6.4.8 Joint
probability 6.5 Water surface elevation spectra 6.5.1
Introduction 6.5.2 Bretschneider and Pierson-Moscowitz spectra
6.5.3 JONSWAP spectra 6.5.4 Effect of alternative frequency
units 6.5.5 Directional spectra 6.5.6 Selection of
spectral shape 6.6 Individual wave scatter diagrams 6.6.1
Introduction 6.6.2 The wave height exceedence method
6.6.3 Individual wave height - period joint probability diagrams 6.7
Wave modeling 6.7.1 Introduction 6.7.2 Basic physics
6.7.3 Mathematical manipulations 6.7.4 Wave theories
6.7.5 Regular wave theories 6.7.6 Linear wave theory
6.7.7 Stokes' wave theories 6.7.8 Cnoidal regular theory
6.7.9 Stream function wave theories 6.7.10 Other regular wave
theories 6.7.11 Selection of suitable regular wave theory
6.7.12 Irregular (but specified profile) wave theories 6.7.13
Random wave theories 6.7.14 Breaking waves 6.7.15 Wave
current interaction 6.8 Hydrodynamic loading 6.8.1
Introduction 6.8.2 Morison's equation 6.8.3 Selection of
Cd and Cm 6.8.4 Diffraction 6.8.5 Interference
6.8.6 Wave slam and slap 6.8.7 Structural motion, hydrodynamic
added mass and damping 6.9 Analysis of structures subject to extreme and
fatigue hydrodynamic loading 6.9.1 Discussion of wave loading on
offshore structures 6.9.2 Sine wave fitting and complex number
methods 6.9.3 Analysis of wave frequency loading and structural
response 6.9.4 Deterministic analysis 6.9.5 Frequency
domain spectral analysis 6.9.6 Time domain spectral analysis with
linear random wave theory 6.9.7 Time domain spectral analysis -
non-linear random wave theory Notation References 7 Vortex-induced
forces 7.1 The forces on stationary circular cylinders 7.2 Flow
speeds for response of cylinders in steady flow 7.2.1 Critical
velocities for cross-flow motion 7.2.2 Critical velocities for
in-line motion 7.3 Structural response in steady flow 7.3.1
Harmonic model 7.3.2 Effective mass per unit length: me
7.3.3 Criteria for vortex-induced response 7.3.4 Predictions of
amplitude of response of risers 7.4 Vortex shedding in waves
7.4.1 Introduction 7.4.2 A stationary cylinder in waves
7.4.3 Effects of irregular waves, cylinder orientation, wave directionality,
currents, roughness and interference 7.4.4 A compliant cylinder in
waves 7.5 Devices for preventing vortex-induced oscillations
7.5.1 Strakes 7.5.2 Shrouds 7.5.3 Fairings
7.5.4 Air bubbles 7.5.5 Structural damping devices 7.6 The
effect of other flow and structural properties 7.7 Flow calculations
7.7.1 Hydrodynamic damping 7.7.2 Computational flow
techniques 7.8 Analysis sequence Notation References 8 Wind
turbulence 8.1 Introduction 8.2 The structure of strong winds
8.2.1 Origin of the wind 8.2.2 Weather systems 8.2.3
The atmospheric boundary layer 8.2.4 Atmospheric stability
8.2.5 Equilibrium 8.2.6 Summary 8.3 Statistical description
of turbulence 8.3.1 Turbulence statistics 8.3.2
Turbulence - single point statistics 8.3.3 Turbulence - two point
statistics 8.4 Wind data 8.4.1 The mean wind 8.4.2
The turbulent gusts 8.4.3 Non-neutral wind conditions 8.5
Turbulence loads 8.5.1 Aerodynamic loading 8.5.2
Aerodynamic damping 8.6 Calculation of response 8.6.1 Theory
8.6.2 Calculation of response - lattice structures 8.6.3
Calculation of response - single members 8.6.4 Extreme value
analysis 8.6.5 Fatigue life analysis 8.7 Choice of method
8.7.1 Comparison of methods 8.7.2 Analysis hints Notation
Bibliography References Annex 8A ESDU data items Annex 8B
Derivation of theory 8.B.1 Turbulence loads (direct method, ESDU
method) 8.B.2 Single-member methods 8.B.3 General methods
9 Installation 9.1 Introduction 9.2 Transportation 9.2.1
Barge motions 9.2.2 Cargo loading and response 9.2.3 Barge
flexibility 9.2.4 Slam 9.2.5 Self-floating substructures
9.3 Launch and up-ending 9.3.1 Jacket launch analysis
9.3.2 Analysis method 9.4 Lift 9.4.1 Single degree of freedom
lift analysis 9.4.2 Computer analysis of crane dynamic response
9.4.3 Selection of load conditions for analysis 9.5 Docking over a
template 9.6 On-bottom stability 9.7 Pile driving 9.7.1
Mathematical analysis 9.8 Installation of gravity structures
Notation References 10 Earthquakes 10.1 Introduction 10.2
Design philosophy for earthquake loads 10.3 Theory 10.3.1 The
response spectrum method - overview 10.3.2 SDOF lumped-mass system
10.3.3 Derivation of response spectra 10.3.4 Use of
response spectra - SDOF structure 10.3.5 MDOF lumped-mass system
10.4 Design data 10.4.1 Accelerograms 10.4.2 Response
spectra 10.4.3 Directionality of loading 10.5 Specification of
design earthquakes 10.5.1 Earthquake magnitude and intensity
10.5.2 Source evaluation 10.5.3 Source-to-site attenuation
10.5.4 Construction of the response spectrum 10.5.5 Site
response analysis 10.5.6 Design data for North Sea sites 10.6
Calculation of structural response 10.6.1 Foundation model
10.6.2 Structure model 10.6.3 Analysis methods 10.6.4
Choice of analysis 10.6.5 Analysis of secondary systems 10.7
Structural configuration for seismic resistance 10.7.1 Global
configuration (jacket structures) 10.7.2 Joint detailing (jacket
structures) 10.7.3 Gravity structures Annex 10A Sources of
accelerogram data Notation Bibliography References 11 Strength
and fatigue 11.1 Introduction 11.1.1 Limit states
11.1.2 Safety factors 11.1.3 Unity checks 11.1.4
Non-linear complications with dynamic analysis 11.2 Strength assessment
11.2.1 Local modes of failure (yield, fracture, buckling)
11.2.2 Yield 11.2.3 Buckling 11.2.4 Beam columns
11.2.5 Joint strength 11.2.6 Deterministic quasi-static strength
analysis 11.2.7 Frequency domain 'spectral' analysis
11.2.8 Response spectra analysis 11.2.9 Avoiding non-linearities in
frequency domain analysis 11.2.10 Possible methods of linearization
11.2.11 Time history analysis 11.3 Fatigue assessment
11.3.1 S-N curves 11.3.2 Miner's rule 11.3.3
Deterministic fatigue analysis 11.3.4 Spectral fatigue analysis
11.3.5 Narrow band spectra 11.3.6 Broad band spectra
11.3.7 Stress concentration factors 11.3.8 Non-linearities which
affect spectral fatigue analysis 11.4 Fracture assessment
11.4.1 Brittle fracture 11.4.2 Application of fracture mechanics to
fast fracture 11.4.3 Crack propagation 11.5 Overall analysis
methods 11.5.1 Dynamic characteristics of environmental loading
11.5.2 Methods of handling the frequency content 11.5.3
Methods of structural analysis 11.5.4 Wave frequency loading
11.5.5 Wave slam and slap 11.5.6 Vortex shedding loading
11.5.7 Wind loading 11.5.8 Earthquake loading Notation
References12 Examples 12.1 Analyses of a single pile platform
12.1.1 Modeling method 12.1.2 Preliminary estimate of natural
period 12.1.3 Foundation model: p-y curves 12.1.4 Time
history dynamic analysis 12.1.5 Secant stiffness, linearized
foundation, for frequency domain dynamic analysis 12.1.6 Linear
frequency domain analysis 12.1.7 Comparison of time and frequency
domain analysis 12.1.8 Fatigue analysis 12.1.9
Semi-probabilistic fatigue analysis 12.1.10 Spectral fatigue
analysis 12.1.11 The 2.5 second rule 12.1.12 Comparison of
fatigue analysis methods 12.2 Dynamic response of a jack-up platform
12.2.1 Problem definition 12.2.2 Outline methodology
12.2.3 Estimation of natural period 12.2.4 Selection of extreme
regular wave 12.2.5 Wave theory 12.2.6 Regular wave
loading 12.2.7 Structural analysis of static response to regular
wave plus current 12.2.8 Results of regular wave analysis
12.2.9 Spectrum for random wave, frequency domain, spectral analysis
12.2.10 Selection of linear wave theory 12.2.11 Calculation of
wave particle kinematics at a range of depths and wave periods
12.2.12 Combination of particle velocities with spectrum to determine the rms
velocity and linearized drag force equation at any location 12.2.13
Mode shape and the consistent natural period 12.2.14 Hydrodynamic
and structural damping 12.2.15 Spectral calculation of additional
dynamic response to loading in the vicinity of the structural natural period
12.2.16 Frequency multiplying effects 12.2.17 Wind force
on the structure 12.2.18 Summation of the separately calculated
deflections 12.3 Vortex shedding example 12.3.1 Basic data
12.3.2 Calculation of mode 1 frequency and mode shape 12.3.3
Calculation of mode 1 reduced velocity, stability parameter and response
12.3.4 Calculation of mode 2 frequency and mode shape 12.3.5
Calculation of mode 2 reduced velocity, stability parameter and response
12.3.6 Calculation of mode 3 frequency and mode shape 12.3.7
Combination of in-line and cross-flow response 12.3.8 Vortex
shedding in waves 12.3.9 Wave synchronized vortex shedding
References 12.4 Wind turbulence example 12.4.1 Extreme
response analysis Static design Direct
method ESDU method WINDSPEC method
Summary 12.4.2 Fatigue life analysis
Omnidirectional analysis (u-component only) Directional
analysis (u-component only) Directional analysis (u and
v-components) Summary 12.5 Earthquake example
12.5.1 Modeling 12.5.2 Member stiffness matrix 12.5.3
Formation of global stiffness matrix 12.5.4 Deflection under a
static horizontal force 12.5.5 Mass matrix 12.5.6
Polynomial method for the calculation of natural frequencies 12.5.7
Vector iteration method for the calculation of mode shapes 12.5.8
Generalized mass for each mode 12.5.9 Spectral displacement and
acceleration for each natural frequency 12.5.10 Response to
horizontal ground acceleration 12.5.11 Response to vertical ground
motion 12.5.12 Summation of directions 12.5.13 Static
coefficient method References Appendix A Complex number representation
of amplitude and phase A. 1 Plotting on the complex phase - phasor
diagrams A. 2 Calculations using 0° and -90° loading and response as
real and imaginary parts A. 3 e A. 4 Negative frequencies A. 5
Complex number multiplication and division A. 6 Complex number
inversion: 1/Z A. 7 Phase lead and lag Appendix B The Gamma Function
Appendix C Consistent units Appendix D Stiffness matrix of a 3-d beam element
Appendix E Useful data and formulas Index